Steffen Börm

For the investigation of hydrothermal systems, fractured reservoirs and gas migration in the seafloor, accurate simulations of circulation processes through porous media are important. They allow reliable predictions and give a useful prognosis of geological hazards. It is a challenging task to develop models that represent the physical situation as well as possible on one hand. On the other hand the numerical solution of these models should be calculated within acceptable time. Especially for flows through porous and fractured media we need the possibility to solve high-resolution 3-D models, but solving 3-D models is much more memory and time consuming than 2-D models. Hence it is my goal to develop a new method for solving these problems. I propose an improved discretization technique and a Conjugate Gradient solver with geometric multi-grid preconditioning. Since the coarse grid will still be very large for complex geometries, I intend to use a hierarchical matrix method as a coarse grid solver in the multi-grid algorithm. Hierarchical matrices are particularly suitable for solving large linear systems in a storage and time efficient way. This allows us to investigate high-resolution models, particularly in fractured and complex media, like a structurally complex basalt layer or depleted oil reservoirs.